COLLOCATION AND QUADRATURE METHODS FOR SOLVING SINGULAR INTEGRAL EQUATIONS WITH PIECEWISE CONTINUOUS COEFFICIENTS

Abstract

The computation schemes of collocation and mechanical quadraturemethods for approximate solving of the complete singular integral equations withpiecewise continuous coefficients and a regular kernel with weak singularity are elab-orated. The case when the equations are defined on the unit circumference of thecomplex plane is examined. The sufficient conditions for the convergence of thesemethods in the spaceL2are obtained.